Calculator Inputs
Enter a measured quantum yield and excited-state lifetime to estimate radiative and non-radiative decay behavior.
Example Data Table
These example values show how the non-radiative rate changes as quantum yield and lifetime vary.
| Sample | Quantum Yield | Lifetime (ns) | kr (s⁻¹) | knr (s⁻¹) | Radiative Lifetime (ns) |
|---|---|---|---|---|---|
| Dye A | 0.80 | 4.0 | 2.0000e+08 | 5.0000e+07 | 5.0000 |
| Dye B | 0.35 | 2.5 | 1.4000e+08 | 2.6000e+08 | 7.1429 |
| Dye C | 0.12 | 1.1 | 1.0909e+08 | 8.0000e+08 | 9.1667 |
| Dye D | 0.92 | 6.8 | 1.3529e+08 | 1.1765e+07 | 7.3913 |
Formula Used
This calculator assumes a simple excited-state model where total decay is the sum of radiative and non-radiative channels.
Quantum yield relation
Φ = kr / (kr + knr)
Lifetime relation
τ = 1 / (kr + knr)
Derived working equations
ktotal = 1 / τkr = Φ / τknr = (1 - Φ) / ττr = 1 / kr = τ / Φτnr = 1 / knr = τ / (1 - Φ)
Use the quantum yield as a fraction in the equations. If you enter a percent, the calculator converts it internally.
How to Use This Calculator
- Enter a sample label so the exported files are easier to identify.
- Input the measured quantum yield as a fraction or a percent.
- Enter the observed fluorescence lifetime and choose its time unit.
- Optionally provide a measured radiative lifetime to compare consistency.
- Select the number of decimal places for displayed values.
- Click the calculate button to show results above the form.
- Review the decay rates, shares, lifetimes, and plotted graph.
- Download the results as CSV or PDF when needed.
FAQs
1) What is non-radiative decay?
Non-radiative decay is excited-state deactivation without photon emission. Energy is lost through vibration, internal conversion, intersystem crossing, collisions, or chemical pathways. A larger non-radiative rate generally lowers fluorescence brightness and observed quantum yield.
2) How do I calculate non-radiative decay from quantum yield?
Use Φ = kr / (kr + knr) and τ = 1 / (kr + knr). With measured Φ and τ, compute kr = Φ / τ and knr = (1 − Φ) / τ.
3) How to calculate quantum yield?
For emission, quantum yield compares emitted photons with absorbed photons. Relative methods compare a sample against a standard using integrated emission, absorbance, and refractive index corrections. Absolute methods commonly use an integrating sphere.
4) How to calculate quantum yield in fluorescence?
Measure the integrated fluorescence signal, keep absorbance low, and compare the sample against a reference with known yield. The corrected emission-area ratio, absorbance ratio, and refractive index factor give the fluorescence quantum yield.
5) How to calculate quantum yield of photocaging group?
Determine how many molecules are released per absorbed photon. Measure product formation using HPLC, UV-Vis, or NMR, measure absorbed light through actinometry or photon flux, then divide reacted molecules by absorbed photons.
6) Why can quantum yield be high while lifetime stays short?
A short lifetime only means total decay is fast. If the radiative pathway still contributes most of that total rate, quantum yield remains high. Lifetime and branching ratio must always be interpreted together.
7) What happens when quantum yield equals one?
In the simple model, Φ = 1 means all decay is radiative, so knr becomes zero. Real systems can still show complications, but the idealized calculation gives complete emission efficiency.
8) Which units should I use for lifetime and decay rate?
Use seconds in the equations and s⁻¹ for rate constants. You may enter fs, ps, ns, µs, ms, or s here, and the calculator converts automatically. Scientific notation is usually best for reported rates.